The Weibull-power cauchy distribution

Model, properties and applications

M. H. Tahir, M. Zubair, Gauss M. Cordeiro, Ayman Alzaatreh, M. Mansoor

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We propose a new three-parameter distribution with increasing, decreasing, reversed-J and upside-down bathtub shaped hazard rate, called the Weibull-power Cauchy distribution. We obtain explicit expressions for the mode, ordinary, negative and incomplete moments, mean deviations, mean residual life, quantile and generating functions, order statistics, Shannon entropy and reliability. We derive a power series for the quantile function using exponential partial Bell polynomials. A useful characterization of the new distribution is also presented. The method of maximum likelihood is used to estimate the model parameters. The importance of the new distribution is proved empirically by means of three real-life data sets.

Original languageEnglish
JournalHacettepe Journal of Mathematics and Statistics
Volume46
Issue number4
DOIs
Publication statusPublished - Jan 1 2017

Fingerprint

Cauchy Distribution
Power Distribution
Weibull
Quantile Function
Mean Residual Life Function
Bell Polynomials
Mean deviation
Hazard Rate
Shannon Entropy
Order Statistics
Power series
Maximum Likelihood
Generating Function
Model
Moment
Partial
Estimate

Keywords

  • Cauchy distribution
  • Half-Cauchy distribution
  • Moments
  • Power Cauchy distribution
  • T-X family
  • Weibull-X family

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Statistics and Probability
  • Geometry and Topology

Cite this

The Weibull-power cauchy distribution : Model, properties and applications. / Tahir, M. H.; Zubair, M.; Cordeiro, Gauss M.; Alzaatreh, Ayman; Mansoor, M.

In: Hacettepe Journal of Mathematics and Statistics, Vol. 46, No. 4, 01.01.2017.

Research output: Contribution to journalArticle

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